Joint Channel Estimation and Error Correction for Finite-State Markov Channels Using Polar Codes

A joint channel estimation and channel coding scheme is presented for finite-state Markov channels using polar codes. Unlike the conventional approach of first estimating all channel parameters and then performing channel decoding separately, the proposed scheme incorporates a subset of reliable estimates of channel parameters into the decoding algorithm and computes decoding metrics averaged over the statistical behavior of the Markov channel. By adapting list decoding (without any inner code), channel estimation and decoding steps can be performed iteratively to boost the reliability of channel estimation as well as error correction. In order to improve the performance even further, a new pilot transmission scheme is developed that utilizes the structure of polar codes and sends pilot symbols along with code symbols. This construction can be viewed as a new family of shortened polar codes that can be of independent interest. Simulation results demonstrate the benefit of the proposed approach compared to existing solutions.

[1]  Ido Tal,et al.  Fast Polarization for Processes With Memory , 2017, IEEE Transactions on Information Theory.

[2]  Eren Sasoglu.  Polarization in the presence of memory , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[3]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

[4]  Prakash Narayan,et al.  Reliable Communication Under Channel Uncertainty , 1998, IEEE Trans. Inf. Theory.

[5]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[6]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[7]  Sergio VerdÂ,et al.  Fading Channels: InformationTheoretic and Communications Aspects , 2000 .

[8]  Liping Li,et al.  Channel Estimation With Systematic Polar Codes , 2018, IEEE Transactions on Vehicular Technology.

[9]  Eren Sasoglu.  Polar Coding Theorems for Discrete Systems , 2011 .

[10]  Van Nostrand,et al.  Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm , 1967 .

[11]  Valerio Bioglio,et al.  Low-Complexity Puncturing and Shortening of Polar Codes , 2017, 2017 IEEE Wireless Communications and Networking Conference Workshops (WCNCW).

[12]  Erdal Arikan,et al.  Systematic Polar Coding , 2011, IEEE Communications Letters.

[13]  Rongke Liu,et al.  Joint Successive Cancellation Decoding of Polar Codes over Intersymbol Interference Channels , 2014, ArXiv.

[14]  Rongke Liu,et al.  Construction of polar codes for channels with memory , 2015, 2015 IEEE Information Theory Workshop - Fall (ITW).

[15]  Alexander Vardy,et al.  List decoding of polar codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.